Volume V develops the mathematical laws of epistemic error cascades in complex synthetic networks. We formulate how unverified hallucinations propagate exponentially through autonomous multi-agent pipelines and demonstrate how cryptographic DAGs eliminate systemic cascade failures.
1. Information Physics & Thermodynamic Erasure
Rolf Landauer demonstrated in 1961 that computation is fundamentally physical. Erasing or modifying information dissipates heat into the environment:
\[ \Delta Q \ge k_B T \ln 2 \]In epistemic governance, false statements, hallucinations, and unverified outputs are not merely harmless text strings—they represent informational entropy that requires significant metabolic and computational work to diagnose, isolate, and erase.
An unregulated network that generates infinite synthetic hallucinations creates a runaway thermodynamic dissipation catastrophe, exhausting the cognitive resources of human verifiers.
2. Mathematical Mechanics of Recursive Error Cascades
Consider an autonomous multi-agent pipeline of depth \(K\), where each agent \(k\) generates an output conditioned on agent \(k-1\). If each stage has an error probability \(\epsilon > 0\), the probability of composite truth \(\mathcal{P}_{\text{true}}\) degrades exponentially:
\[ \mathcal{P}_{\text{true}}(K) = (1 - \epsilon)^K \approx e^{-K \epsilon} \]For \(K=10\) and \(\epsilon=0.15\), \(\mathcal{P}_{\text{true}} \approx 0.197\)—meaning over \(80\%\) of multi-step autonomous pipelines without formal verification result in catastrophic falsehoods.
3. Acyclic Cryptographic Provenance DAGs
The only mathematical cure for recursive error cascades is the enforcement of a Directed Acyclic Graph (DAG) of Cryptographic Provenance:
\[ \mathcal{G} = (V, E, \mathcal{H}), \quad \text{where} \quad v_i = \text{SHA256}\left( \text{data}_i \parallel \text{parents}(v_i) \right) \]Every synthetic proposition must carry a cryptographically signed proof trace verifying:
- The exact model checkpoint, prompt, temperature, and random seed.
- The exact retrieval sources and mathematical citations.
- The verification certificate from a deterministic symbolic evaluator.
Any node lacking a valid certificate is rejected before memory consolidation, truncating error propagation at depth \(K=1\).
4. Zero-Trust Epistemic Governance
Epistemic governance treats every synthetic output as unverified until proven otherwise. This replaces naive trust with mathematical verification:
\[ \text{Verdict} = \operatorname{Eval}_{\text{symbolic}}\left( \text{Output} \wedge \text{Invariant}_{\text{constitutional}} \right) \]By separating the creative generation engine (neural LLMs) from the deterministic verification engine (symbolic math engines, type checkers, theorem provers), sovereign systems achieve flawless reliability.
5. Falsifiable Predictions & Reliability Bounds
- Cascade Bound: Pipelines with cryptographic DAG verification achieve zero compounding error across arbitrary depths \(K \ge 50\).
- Energy Reduction: Pre-filtering invalid propositions reduces downstream verification compute by \(\ge 65\%\).
- Auditability: 100% of state transitions can be reconstructed and verified offline.